Formula for a simple S Curve

[jerH]

I need to be able to generate a simple S-shaped curve for x and y values that both range from 0 to 1.

The idea is that this is the graph of the "value" obtained (the y-axis) if you fund a project at various levels from 0 to 100% (the x-axis).

It should start by rising fairly slowly, then start to grow quickly through the middle part of the domain, then flatten out toward the end.

I suspect there will be one or more parameters that the formula requires to control the general shape. I need to be able to tune those parameters so that my customer agrees with the shape of the graph...then I'll have the formula so that I can plug in a funding level and get out a value score.

I know the general formula for an s curve is 1/(1+e^-x)...but this isn't bound to my domain or range, and my math isn't good enough to figure it out myself.

I'm perfectly happy to implement this as two exponential functions, one that covers the left portion of the domain, and one that covers the right.

I hope this is clear....please feel free to tell me if it isn't.

 

[StephenCrump]

shg's post # 5 here may be helpful: http://www.mrexcel.com/forum/excel-questions/828290-distribute-number-across-cells.html

 

[jerH]

Thanks for that...I found another example here that I've been able to massage until it's close...

It takes two sets of inputs, a point on the lower end of the domain and the corresponding y-value, and a point on the upper end of the domain and the corresponding y-value. However, it was meant for market penetration and so when x is 0, y is ~2.5% (instead of 0) and when x is 1, y is 97.5% (instead of 1)...

In excel the formula looks like this

1/(1+EXP(-((LN(1/Value1-1)-LN(1/Value2-1))/(Time2-Time1))*(XValue-(LN(1/Value1-1)/((LN(1/Value1-1)-LN(1/Value2-1))/(Time2-Time1))+Time1))))

where the two anchor points are (Time1, Value1) and (Time2, Value2) and XValue is the point on the X-axis being evaluated

If I knew enough to force this through the origin and (1,1) I'd be in business.....